# Linear Leaky-Integrate-and-Fire Neuron Model Based Spiking Neural Networks and Its Mapping Relationship to Deep Neural Networks

arXiv: https://arxiv.org/abs/2207.04889 · HTML: https://mlsanity.com/paper/2207.04889/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 73 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Object Detection with Deep Learning: A Review](https://mlsanity.com/paper/1807.05511/) (2018)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Spiking-YOLO: Spiking Neural Network for Energy-Efficient Object Detection](https://mlsanity.com/paper/1903.06530/) (2019)
- [RMP-SNN: Residual Membrane Potential Neuron for Enabling Deeper High-Accuracy and Low-Latency Spiking Neural Network](https://mlsanity.com/paper/2003.01811/) (2020)
- [Enabling Deep Spiking Neural Networks with Hybrid Conversion and Spike Timing Dependent Backpropagation](https://mlsanity.com/paper/2005.01807/) (2020)
- [SipMask: Spatial Information Preservation for Fast Image and Video Instance Segmentation](https://mlsanity.com/paper/2007.14772/) (2020)
- [Towards an integration of deep learning and neuroscience](https://mlsanity.com/paper/1606.03813/) (2016)
- [Dynamic ReLU](https://mlsanity.com/paper/2003.10027/) (2020)
- [Conversion of Artificial Recurrent Neural Networks to Spiking Neural Networks for Low-power Neuromorphic Hardware](https://mlsanity.com/paper/1601.04187/) (2016)
- [Biologically plausible deep learning -- but how far can we go with shallow networks?](https://mlsanity.com/paper/1905.04101/) (2019)
- [STDP-based spiking deep convolutional neural networks for object recognition](https://mlsanity.com/paper/1611.01421/) (2016)
- [First-spike based visual categorization using reward-modulated STDP](https://mlsanity.com/paper/1705.09132/) (2017)
- [Training Spiking Deep Networks for Neuromorphic Hardware](https://mlsanity.com/paper/1611.05141/) (2016)
- [Unsupervised Visual Feature Learning with Spike-timing-dependent Plasticity: How Far are we from Traditional Feature Learning Approaches?](https://mlsanity.com/paper/1901.04392/) (2019)
- [Bio-Inspired Spiking Convolutional Neural Network using Layer-wise Sparse Coding and STDP Learning](https://mlsanity.com/paper/1611.03000/) (2016)
- [Representation Learning using Event-based STDP](https://mlsanity.com/paper/1706.06699/) (2017)
- [Cascaded Subpatch Networks for Effective CNNs](https://mlsanity.com/paper/1603.00128/) (2016)

## Built on by (most cited first, 8 of 8)

- [How important are activation functions in regression and classification? A survey, performance comparison, and future directions](https://mlsanity.com/paper/2209.02681/) (2022)
- [Sign Gradient Descent-based Neuronal Dynamics: ANN-to-SNN Conversion Beyond ReLU Network](https://mlsanity.com/paper/2407.01645/) (2024)
- [Detection of Fast-Moving Objects with Neuromorphic Hardware](https://mlsanity.com/paper/2403.10677/) (2024)
- [Scaling Up Resonate-and-Fire Networks for Fast Deep Learning](https://mlsanity.com/paper/2504.00719/) (2025)
- [Neuromorphic Correlates of Artificial Consciousness](https://mlsanity.com/paper/2405.02370/) (2024)
- [SteganoSNN: SNN-Based Audio-in-Image Steganography with Encryption](https://mlsanity.com/paper/2511.06573/) (2025)
- [Benchmarking Storage Systems for Machine Learning Workloads Using NIO Bench](https://mlsanity.com/paper/2609.05418/) (2026)
- [DVA-Neurons: Design and Verification of Adaptive LIF Neurons: From Single-Neuron Dynamics to Multi-Neuron Spiking Networks](https://mlsanity.com/paper/2609.22775/) (2026)

## Abstract (arXiv)

Spiking neural networks (SNNs) are brain-inspired machine learning algorithms with merits such as biological plausibility and unsupervised learning capability. Previous works have shown that converting Artificial Neural Networks (ANNs) into SNNs is a practical and efficient approach for implementing an SNN. However, the basic principle and theoretical groundwork are lacking for training a non-accuracy-loss SNN. This paper establishes a precise mathematical mapping between the biological parameters of the Linear Leaky-Integrate-and-Fire model (LIF)/SNNs and the parameters of ReLU-AN/Deep Neural Networks (DNNs). Such mapping relationship is analytically proven under certain conditions and demonstrated by simulation and real data experiments. It can serve as the theoretical basis for the potential combination of the respective merits of the two categories of neural networks.